Next, we turn our attention to the helicity conservation (REF ) in the Euler equations.
The concept of the
helicity in an inviscid fluid was introduced by Moffatt in [1]}. As pointed in [1]}, [3]},
helicity is important at a fundamental level in relation to flow kinematics
because it admits topological interpretation in relation to the linkage or
linkages of vortex lines of the flow.
Indeed,
Moffatt [1]} examined that the helicity of smooth solutions to
the following compressible Euler equations (REF ) is invariant in time,
\(\left\lbrace \begin{aligned}&\rho _t+\nabla \cdot (\rho v)=0, \\&(\rho v)_{t} +\mathrm {div}\,(\rho v\otimes v)+\nabla \pi (\rho )=0.\end{aligned}\right.\) 
